What is the Black-Litterman model?

The biggest new feature of AllocationADVISOR 6.0 is the inclusion of the BlackLitterman model. The Black-Litterman model was created by Fischer Black and RobertLitterman of Goldman Sachs. Conceptually, it combines a number of the pillars ofmodern portfolio theory Sharpes CAPM and Markowitzs mean-variance optimization.The Black-Litterman model is not an alternative or a replacement of mean-varianceoptimization; it is a tool for creating a set of expected returns for use within themean-variance optimization framework.Harry Markowitzs mean-variance optimization is the heart of modern asset allocation.Unfortunately, a number of people dont use mean-variance optimization because theresulting asset allocations are highly concentrated in just a few of the assets beingoptimized. The Black-Litterman model eliminates this problem by creating betterestimates of expected return that carefully balance risk and return, leading to welldiversified portfolios.For more information about how the Black-Litterman Forecast Model leads to diversifiedportfolios, see the article Black-Litterman: Asset Allocations You Can Actually Use!For a discussion about how the Black-Litterman model calculates forecasts, see Howdoes the Black-Litterman Model Calculate Return Forecasts?

How do you create a Black-Litterman Asset Allocation Case?

We have gone to great efforts to make this sophisticated model easy to use. To create anAsset Allocation case using the Black-Litterman Forecast model, after naming theAllocation Case and selecting the Black-Litterman Forecast Model, you begin byselecting the assets to optimize. Zephyr groups some of the most popular asset classestogether in what we call Asset Palettes. Technically, Asset Palettes are collections ofMarket Cap Assets, where Market Cap Assets are asset class index proxies that are linkedto an estimate of the market capitalization of the asset class in question. Using AssetPalettes created by Zephyr makes it very easy to select a logical set of asset classes.Zephyr-created Asset Palettes are groups of non-overlapping asset classes that representreasonable market portfolios or segments of a market portfolio. AllocationADVISORalso allows users to create Custom Palettes. The ability to select a predefined AssetPalette can dramatically decrease the time required to create an asset allocation analysis.After selecting the Asset Palette, you need to enter a Risk-Premium and a Risk-Free Rate.For those that need assistance in estimating these values we provide the historical 10, 25,and 50 year risk premia on six model portfolios, as well as the annual yield on the 3month, 1-year, 5-year, and 10-year US Treasuries. The historical risk-premia and annualyield data is updated monthly and distributed with Zephyrs Full Index Update.

Select anAssetPalette

EnterPalette RiskPremium

EnterRisk-FreeRate

We encourage you to select

your own Palette RiskPremium and Risk-Free Rate.For those who needassistance selectingappropriate values, these twodialog boxes provideguidance.

After specifying a Palette Risk Premium and a Risk-Free Rate, all that you need to do isselect Done and an Efficient Frontier graph and Inputs table for the Allocation Case areadded to your workbook.

How do you incorporate your unique forecasts of returns?

For those of you who wish to modify the return forecasts to match your own opinionsabout future market performance, the Black-Litterman model provides an elegantframework for combining a base case set of market implied returns with your uniqueforecasts. The new mixed Forecast Returns still lead to well-diversified portfolios thatreflect your opinions.Your unique forecasts of expected returns are called Views. There are two types ofViews Absolute Views and Relative Views each of which is entered on theirrespective windows in the Allocation Case tree.Absolute Views state your unique return forecast of an asset class or group of assetclasses. For example, US Small Cap will have a return of 11.5%.

Enter ViewReturn andConfidence

US Small Cap is actually a combination of two asset classes US Small Cap Growth andUS Small Cap Value. The formation of View Groups gives you greater flexibility forspecifying views.

View Groups give

you greaterflexibility forspecifying views

Relative Views specify the expected return differential between two asset classes / viewgroups. For example, US Large Cap Growth will outperform US Large Cap Value by1%.

Enter ViewReturn andConfidence

For both types of views, you need to specify a confidence level between 5% and 95%.This confidence level represents the strength of your view. All else equal, the moreconfidence you assign to a View, the more aggressively the model will implement thatview.Once you have specified your views, select Done.

How do you show two efficient frontiers on the same graph?

One of the most requested features that has been added to AllocationADVISOR is theability to show two efficient frontiers on the same graph.

In addition to two efficient frontier graphs, you can also plot the benchmark on theEfficient Frontier graph. The efficient frontier options are available from a right-clickmenu.

Multiple Custom Portfolios

AllocationADVISOR 6.0 allows users to enter multiple custom portfolios in theirallocation cases. These can be any portfolio that users wish to compare to the efficientportfolios, such as a current portfolio or a target portfolio. Users can select which of thecustom portfolios will be the Comparison Portfolio, which can be displayed on many ofthe graphs and tables.

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Monte Carlo Enhancements

We also made two enhancements to the Monte Carlo Simulations for this release. Thefirst is the ability to enter moving average cash flows. We have also changed the colorson the Simulation Probability graph, making it easier to distinguish between the differentprobabilities.

ConclusionAllocationADVISOR 6.0 includes the Black-Litterman model, one of the mostsophisticated asset allocation models. Best of all, we have removed the complexityassociated with the model making it intuitive and very easy to use. At last, you will beable use a mean-variance optimizer and feel good about the resulting allocations. A copyof the workbook used to create the sample illustrations is available on our web site in theHTML version of this article.(http://www.styleadvisor.com/resources/newsletters/NewInAA.html)For additional information on the Black-Litterman model, see the article The BlackLitterman: Asset allocation you can actually use!(http://www.styleadvisor.com/resources/newsletters/BLPortfolios.html)

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Black-Litterman: Asset Allocations You Can Actually Use!

Have you given up on mean-variance optimization because the resulting asset allocationsare unintuitive and anything but diversified? Or perhaps you feel the need to use meanvariance optimization coupled with tight optimization constraints? The inclusion of thesophisticated Black-Litterman asset allocation model into AllocationADVISOR will helpyou realize the benefits of mean-variance optimization.Portfolios created using the Black-Litterman approach and mean-variance optimizationare well diversified and intuitively reflect the investors own forecasts about futuremarket performance.Harry Markowitzs mean-variance optimization is widely regarded as the holy grail ofasset allocation. Markowitzs seminal work demonstrated how to form efficientportfolios based on three inputs returns, standard deviation, and correlations. His workresulted in a Nobel Prize. Unfortunately, Markowitz never told us how to derive theinputs, especially the estimated expected returns.Unlike a number of other Nobel Prize winning ideas, mean-variance optimization has notenjoyed a high level of practitioner acceptance. This is because the Markowitz algorithmis very powerful, perhaps too powerful for its own good. The algorithm is very sensitiveto the return forecasts, which have traditionally been created using historical returns. Iftwo asset classes are similar, but one has a slightly higher forecasted return, the optimizerallocates everything to the asset with the higher forecasted return and nothing to the otherasset. Because of this input sensitivity, mean-variance optimizers can lead to highlyconcentrated asset allocations that contradict the common sense notion of diversification.The input sensitivity also makes it difficult for investors to incorporate their ownforecasts into a historical model.Many investors have attempted to overcome these shortcomings in mean-varianceoptimization by using tight constraints on the optimization. These artificial limitsinterfere with the optimization in a way that renders the output sub-optimal. The tighterthe constraints, the further you move toward dictating the allocations to the optimizerinstead of optimizing the allocations. The Black-Litterman model, on the other hand,creates better return forecasts so that it is not necessary to constrain the optimization inorder to create diversified portfolios. This allows investors to harness the power ofmean-variance optimization in a practical and intuitive way.In the first section below we take a closer look at the poorly diversified asset allocationsthat typically result from using purely historical inputs. Next we look at the solution, theBlack-Litterman model, and the well-diversified asset allocations that result from usingreturns from the Black-Litterman model. In the second section below we demonstratewhy the Black-Litterman approach to incorporating investors forecasts of future marketperformance is superior to an ad-hoc approach.

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Diversified PortfoliosInvestors have traditionally used historical returns, standard deviations and correlationsas the inputs for mean-variance optimization. Figure 1 shows an efficient frontier createdusing eight years of historical data (the longest period available for this set of indices) forthe forecasts.Figure 1: Efficient Frontier Based on Historical Returns

While this appears to be a perfectly usable efficient frontier, an examination of the

allocations of the portfolios along the frontier shows that they are poorly diversified.Figure 2 compares five asset allocations of five mixes corresponding to the approximatestandard deviation levels 5%, 7.5%, 10%, 12.5%, and 15%.Figure 2: Asset Allocation Mixes Based on Historical Returns

Historical Returnslead toconcentratedportfolios

Of the eight available asset classes, none of the optimal asset allocation mixes containmore than two asset classes. Historical returns lead to poorly-diversified assetallocations!

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Recall that the goal of mean-variance optimization is to capture the benefit of

diversification and to find asset allocations that maximize expected return for a givenlevel of risk. Fortunately, there is a solution, albeit a solution that emerged almost 50years after the creation of mean-variance optimization. AllocationADVISOR 6.0 has abetter tool for estimating expected returns the Black-Litterman model.The Black-Litterman approach tackles the weakest point of mean-varianceoptimizationits sensitivity to the return forecasts. Black-Litterman uses the historicalstandard deviations and correlations, values which tend to be stable and make goodforecasts, but develops better estimates of expected returns.The foundation of the Black-Litterman model is the Implied Returns. To calculate theImplied Returns we define the market as the set of assets available to the investor. TheImplied Returns are calculated by assuming that the market is in equilibrium (supply forthe assets equals demand) and by using reverse optimization to back out the returns thatwould bring about this equilibrium. These calculations require three pieces ofinformation for the marketthe risk premium, covariance and market capitalizations ofthe assets.If the investor does not wish to add their own views to the forecasts, the Implied Returnsare the Black-Litterman forecasts and are used to create the efficient frontier. Figure 3shows an efficient frontier created using Implied Returns.Figure 3: Efficient Frontier Based on Black-Litterman Returns

The superior diversification of the asset allocation mixes that result from the BlackLitterman Implied Returns is demonstrated in Figure 4.

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Figure 4: Asset Allocation Mixes Based on Black-Litterman Returns

Black-LittermanImplied Returnslead to diversifiedportfolios

Of the eight asset classes, all of the optimal asset allocation mixes contain six or moreof the eight asset classes.Customizing the Implied Returns with ViewsAs demonstrated above, the Implied Returns are excellent forecasts for use with meanvariance optimization. Investors, however, often have their own opinions about how themarket is going to behave in the future. These investors often want to adjust the ImpliedReturns so that the forecasts better reflect their opinions, or views, on futureperformance.How should an investors views be incorporated into the return forecasts? Why not justdirectly edit the Implied Returns so that they reflect the views? As we demonstratebelow, trying to edit the Implied Returns directly leads once again to non-diversifiedportfolios. The Black-Litterman model, on the other hand, gives you an intuitive way toincorporate views without losing the advantage of diversification which comes fromusing the Implied Returns.For our examples we will use two sample views:View 1: US Large Cap Value will outperform US Large Cap Growth by 1%View 2: US Small Cap will have a return of 11.5%These Views can be better understood by comparing them to the Implied Returns. TheImplied Returns forecast that US Large Cap Value will under perform US Large CapGrowth. View 1, then, is a bullish relative view on US Large Cap Value relative to USLarge Cap Growth. View 2 reflects the investors bullish view on US Small Cap. Why?Because the View return of 11.5% is greater than the Implied Return for US Small Cap(the weighted average of US Small Cap Growth and US Small Cap Value) which is10.92%.Lets look at one possible ad-hoc approach to implementing these views as an example.For View 1, we could increase the return of US Large Cap Value and simultaneouslydecrease the return of US Large Cap Growth until the difference is 1%. And for View 2,we could increase the return of the two components of US Small Cap so that the weightedaverage return equals 11.5%. Figure 5 shows the resulting efficient frontier and mixes.

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Figure 5: Efficient Frontier and Mixes (Ad-hoc Approach)

Ad-hoc approachesto incorporatingviews lead toconcentratedportfolios

We can see from the allocations in Figure 5 that even though we started with the BlackLitterman Implied Returns, which we have seen lead to well-diversified asset allocations,the ad-hoc approach to incorporating the views leads to relatively concentrated assetallocations.The Black-Litterman model offers an alternative to this kind of ad-hoc adjustment of thereturn forecasts. The Black-Litterman model uses a sophisticated mixed estimationtechnique to incorporate views into return forecasts which continues to derive returns as arelatively balanced function of risk. The result is diversified portfolios whose allocationsreflect the views of the investor.Figure 6 shows the mixes created by using the Black-Litterman approach to incorporateour two sample views.

Figure 6: Asset Allocation Mixes Based on Black-Litterman Approach

Notice in Figure 6 that at each of the five standard deviation levels we have achievedimproved diversification using the Black-Litterman model relative to the ad-hocapproach.

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The other advantage to using the Black-Litterman approach to include views in theoptimization is that the resulting portfolios are affected in an intuitive way. This meansthat if you are bullish on Small Cap, the mixes will increase the allocation to Small Capby a reasonable amount. While this may sound like an obvious (and necessary) result,those of you who have attempted to adjust return forecasts manually will recognize that itis not necessarily easy to achieve.Figure 7 compares the asset allocation mixes at each of the five standard deviation levelsusing the Black-Litterman case without views (just using the Implied Returns) and theBlack-Litterman case with views.Figure 7: Asset Allocation Mix Comparison

The upper panel of Figure 7 shows the allocations using the Black-Litterman approachwithout views while the lower panel shows the allocations using the Black-Littermanapproach with our two sample views. Remember that the sample views were bullish onUS Large Cap Value and Small Cap. Note that the allocations reflect these views in anintuitive way, with increased allocations to these two assets.Whats NextHopefully by now you are anxious to start using the AllocationADVISORs BlackLitterman Forecast Model. If you havent already done so, you will need to downloadAllocationADVISOR 6.0. The AllocationADVISOR workbook file that was used tocreate all of the examples in this newsletter is available for download on the html versionof this article: http://www.styleadvisor.com/resources/newsletters/BLPortfolios.html

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We will be hosting a number of AllocationADVISOR 6.0 WebEx online training

sessions. Our online training schedule is available on our website at:http://www.styleadvisor.com/training.For a non-technical discussion of how the Black-Litterman model calculates forecasts,see How does the Black-Litterman Model Calculate Return Forecasts?For those of you who would like to know more about the mathematics of the BlackLitterman model and our implementation of it, go to the Black-Litterman ForecastMethodology section of the AllocationADVISOR manual. This section of the manualexplains reverse optimization, the process of creating Market Cap Assets, and the ZephyrAsset Palettes. The AllocationADVISOR manual is located in your Style folder as wellas the Start Menu StyleADVISOR Program Group.For the mathematically inclined, a copy of A Step-By-Step Guide to the BlackLitterman Model: Incorporating User-Specified Confidence Levels is available uponrequest (support@styleadvisor.com).

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How does the Black-Litterman Model Calculate Return Forecasts?

Several techniques for creating better return forecasts for use with mean-variance optimizationhave been developed recently. We believe that we have found the best of these solutions andwe have incorporated it into AllocationADVISOR. The Black-Litterman forecast model createsreturn forecasts which are based on sound economic theory and which help harness the powerof mean-variance optimization. Using Black-Litterman return forecasts in mean-varianceoptimization results in intuitive, diversified portfolios which are relevant for practical investing.For more information about how Black-Litterman leads to diversified portfolios, see the articleBlack-Litterman: Asset allocations you can actually use! located on our website at:http://www.styleadvisor.com/resources/newsletters/BLPortfolios.htmlHow does the Black-Litterman method create return forecasts?The model uses a technique called reverse optimization to determine the Implied Returns of aportfolio based on the available market capitalization of the asset classes being optimized. Italso provides a framework to mix investor views with the Implied Returns to form a newcombined estimate of returns.

Implied ReturnsBlack-Litterman return forecasts are based on the Implied Returns. Implied Returns is aconcept which is based on market equilibrium. The investor first selects an asset palette, whichis the set of assets that will be optimized. This asset palette is assumed to be the market. Wefurther assume that the market is in equilibrium. Equilibrium really means that the marketprice is such that supply equals demand. In this case, we are assuming that the supply of assetsis equal to the demand for the assets. When we are talking about assets, the price becomes areturn. It is the return that is implied by the market equilibrium that we want to find. This is theImplied Returns.What is the market equilibrium? If we believe in efficient markets, then the market today is inequilibrium. The equilibrium portfolio, then, is the market portfolio. The market portfolio isthe capitalization-weighted portfolio of the assets.Most of the time investors will use multiple asset classes when creating an asset allocation. Inorder to demonstrate the mathematics behind the model without resorting to matrix algebra(which is beyond the scope of this article) we will look at a simple three asset example:AssetUS EquityUS BondsIntl Equity

Market Cap$ 11,498$ 8,280$ 10,350

The Implied Returns, as the name suggests, are the returns which are implied by the capweighted market portfolio. The Implied Returns are calculated using reverse optimization.This is sometimes referred to as backing out the returns. There are three components of the

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calculation of Implied Returns, the Risk Aversion Coefficient, the Covariance Matrix and theMarket Portfolio Weights.To start, we will calculate the Implied Excess Returns. At the end we will convert these toTotal Returns. In order to keep this article as user-friendly as possible, we will spell out asmuch as possible, and avoid using symbols.Implied Excess Returns = Risk Aversion Coefficient * Covariance * Market Capitalization Weights

Lets look at the three components of this calculation.

The Risk Aversion Coefficient (RAC)The Risk Aversion Coefficient (RAC) is the rate at which more return is required for more risk.It is the palette risk premium divided by the variance of the asset palette. The variance iscalculated using the historical returns for the assets. The risk premium is entered by the user.Risk Premium

Risk Aversion Coefficient =

Variance

The forward looking Risk Premium is one of the most contentious topics in finance. The equityRisk Premium is the expected excess return of equity over the Risk-Free Rate. For thecalculation of the Implied Returns, the Risk Premium is an estimate of the Asset Palettesexcess return over the Risk-Free Rate. The Asset Palette Risk Premium acts as a scaling factorin the reverse optimization process. While we recommend that you select a reasonable number,the actual number (assuming it is positive) will not change the composition of the efficientallocations that form the efficient frontier. What is affected by the Risk Premium is themagnitude of the return forecasts. An unrealistic Risk Premium results in unrealistic forecastreturns leading to unrealistic conclusions regarding future wealth.For our three asset example we will forecast a Risk Premium of 4%. The Variance of the AssetPalette is 1.117%.Risk Aversion Coefficient =

4.00%1.117%

= 3.404

Covariance (Cov)The covariance (COV) measures the correlation in the fluctuation of the return series. The mostcommon example of this is the performance of equity and fixed income. It is generally acceptedthat when equity is performing well, fixed income yields tend to be lower. Conversely, whenequity is not performing well, fixed income yields are higher. The covariance captures thisrelationship between assets.The covariance of each pair of assets is calculated using historical correlations and standarddeviations. So, the covariance of Assets A and B is:Covariance (A,B) = Correlation (A,B) * Standard Deviation (A) * Standard Deviation (B)

Market Portfolio Weights (MPW)

For the calculation of the Implied Returns we are assuming that the market is in equilibrium.The equilibrium portfolio is the Market Portfolio. The weights of each of the assets in theMarket Portfolio are calculated using the market capitalization of each of the assets. The weightgiven to each asset is proportional to the assets share of the total market cap of the MarketPortfolio. These weights are called the Market Portfolio Weights.In AllocationADVISOR, users can either select to use assets for which we provide monthlymarket cap estimates, or create their own data series with a market capitalization value.For our three assets, the market caps and weights look like this:

US EquityUS BondsIntl EquityTOTAL

Market Cap$ 11,498$ 8,280$ 10,350$ 28,980

MPW38.2%27.5%34.4%100%

As an example, we can look at the calculation of the weight for US equity:

MPWUSEquity =

US Equity Market Cap

Total Market Cap

11,498

28,980

.382

Implied Excess Returns (IER)

Now that we have the three necessary pieces, lets put them together and calculate the ImpliedReturns. Due to the nature of the covariance matrix-the second element in the formula-thecalculations are generally made using matrix algebra. It is for this reason that we have chosen

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to use a three asset example in this article. We can now break down the formula for ImpliedExcess Returns without having to resort to matrix algebra:

IERUSEquity = RAC *

[ Cov(US Equity, US Equity) *

MPWUS Equity

+ Cov(US Equity, US Bonds) * MPWUS Bonds

+ Cov(US Equity, Intl Equity) * MPWIntl Equity ]

= 3.404 * [.036*.382 + .002*.275 + .010*.344] = 6.05%

Implied ReturnsThe final step is to turn this Implied Excess Return into a Total Return. To do this, the investormust make an estimate of the risk-free rate of return. Here, we will use a risk-free rate of 4.5%.Implied Return = Risk-Free Rate + Implied Excess ReturnImplied Return for US Equity = 4.50 + 6.05 = 10.55%The Implied Return of the other assets is calculated in the same way.

US EquityUS BondsIntl Equity

ImpliedReturn10.6 %5.2 %8.9 %

These implied returns can now be used as return forecasts for mean-variance optimization. Themaximum Sharpe ratio portfolio on an efficient frontier created using Implied Returns is themarket portfolio as you defined it. The fact that the Black-Litterman model recommendsholding the market portfolio if you do not have Views is, from a theoretical standpoint, veryappealing. Movements away from market capitalization weighted holdings are based on Views.ViewsThe Implied Returns are excellent forecasts for use with mean-variance optimization. Investors,however, often have their own opinions about how the market is going to behave in the future.These investors often want to adjust the Implied Returns so that the forecasts better reflect theiropinions on future performance.The Black-Litterman method takes an opinion such as I think that US Equity is going to dowell, and quantifies it into something called a View. For this Absolute View, what this reallymeans is that US Equity is going to do better than the 10.6 % forecasted in the Implied Returns.The user must decide how much better US Equity will perform, and assign a level of confidenceto the View. The View may then be I believe with 75% confidence that US Equitys returnwill be 11.5%.23

Users can also create relative Views. The opinion might therefore be Intl Equity willoutperform US Equity. The Implied Returns forecast the opposite, that US Equity willoutperform Intl Equity. Again, the user must enter the amount of out-performance and aconfidence level. An example is I believe with 85% confidence that US Bonds willoutperform US Equity by 1%.How are these views incorporated into the return forecasts? The Black-Litterman model uses aBayesian approach to incorporating Views into the forecasts while maintaining the advantage ofdiversification which comes from using the Implied Returns.The mathematics of Bayesian probabilities is complicated, but the idea behind it is fairlystraightforward. Bayesian probabilities were designed to incorporate subjective beliefs intoprobability distributions. The user starts with a belief, called the Prior distribution. There isthen some event which provides more information, causing the user to wish to modify thedistribution. The event is incorporated into the Prior to form the new belief, the PosteriorDistribution.When creating return forecasts for mean-variance optimization, the Prior and Posteriordistributions are return distributions. The Prior distribution is the Implied Return distribution.The events that are incorporated into the Prior distribution are the investors Views. The newcombined return distribution is the Posterior Distribution. These are the returns that are used asforecasts for mean-variance optimization.Implied Returns

Views

Black-Litterman ForecastReturnsFor those of you who would like to know more about the mathematics of the Black-Litterman model and ourimplementation of it, go to the Black-Litterman Forecast Methodology section in the AllocationADVISOR manual.This section of the manual explains reverse optimization, the process of creating Market Cap Assets, and theZephyr Asset Palettes. The AllocationADVISOR manual is located in your Style folder as well as the Start MenuStyleADVISOR Program Group.For the mathematically inclined, a copy of A Step-By-Step Guide to the Black-Litterman Model: IncorporatingUser-Specified Confidence Levels is available upon request (support@styleadvisor.com).

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Home Prices in StyleADVISOR

You cant pick up a newspaper today without reading about the boom in single family homeprices. It is, therefore, timely that Zephyr should add a home price data base to the ever growinglist of over 12,000 indexes found in StyleADVISOR. This database includes home pricequarterly returns for fifty states, ten regions and 379 cities starting in 1975. These returns arecomputed by the Office of Federal Housing Enterprise Oversight (OFHEO). Our interest in homeprices was prompted by the announcement that the Chicago Mercantile Exchange will begintrading derivatives on home prices in selected cities. These instruments will allow home ownersto hedge their real estate exposure. Even those who have no interest in these new securities (to beissued sometime in 2005) should find the home indexes a useful addition to StyleADVISOR.There are a number of ways that the home price data can be displayed in StyleADVISOR. Figure1 plots the home price index for Fort Lauderdale (this index also includes Pompano andDeerfield Beach) in our Performance graph along with the aggregate home price index for theentire United States. This is the growth of $100 starting December 1, 1975. The red shaded areaat the bottom of the graph measures the cumulative difference between Fort Lauderdale homeprices and the rest of the country. The fact that the cumulative difference was negative for all thisperiod means that home prices in Fort Lauderdale lagged the country. Figure 2 shows thisrelationship broken up into shorter time periods. Here we see the rolling five year differencebetween Fort Lauderdale (blue line) and the US (black line). For a short time in the early 1980sFort Lauderdale prices outperformed the US but for the rest of the 80s and all of the 90s priceslagged most of the rest of the country. Since 2001 there has been a sharp increase in FortLauderdale prices relative to the US. In the five year period ending December 2004, FortLauderdale outperformed the US by 6.29% annually. Many believe that this recent relativestrength in Florida real estate is due to the growing retirement of the baby boomers. This couldcertainly be a factor, but it doesnt explain the same phenomenon occurring in places likeBakersfield, Baltimore, Providence RI and many other non-retirement cities.Figure 1

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Figure 2

Another way to compare Fort Lauderdale and US home prices is to look at the calendar yearreturns, as seen in Figure 3. It is interesting to note that the single best calendar year for FortLauderdale was 1980 when home prices increased by 19.02%. The best calendar year for overallUS prices was 1978 with home prices appreciating by 13.32%.Figure 3

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Figure 4 looks at rolling four quarter (one year) rates of return. We think this graph does the bestjob of putting the recent strength in real estate prices into a longer term perspective. Here we cansee that the worst one year return for Fort Lauderdale was the one year ending September 30,1984 with home prices down 3.37%. The strongest one year period is the one ending September30, 2004 with prices up 23.89%. Even if we are reluctant to call the recent price appreciation abubble, we have to admit that the last few years have not been typical. After a similar price spikeup in 1980, year-to-year home prices in South Florida (as in the US as a whole) were quitemodest. The annual compound growth rate for Fort Lauderdale home prices for the seventeenyears ending December 1999 was 2.37% and for the US was 4.26%.Figure 4

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Figure 5 shows four tables that we prepared using the search function in StyleADVISOR thatshow the best and worst housing markets for the last five and three year periods.Figure 5

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Using the four graphs (Figures 1-4) we have discussed, we have created two new workbooks thatcan be downloaded from our website in the Workbooks section (non-Zephyr clients candownload PDF versions of the workbooks). One workbook incorporates four graphs on one pagefor each of the fifty states. A second workbook uses the same analysis for the largest 25 cities. Ofcourse, Zephyr clients can create their own analysis for any of the 379 cities.Technical Notes for StyleADVISOR UsersTo create the graphs in this example we selected Fort Lauderdale from the Home Prices databaseas our manager. For the benchmark we selected the United States returns from the samedatabase. Figure 2 is our Custom Axis graph. For the Y axis we selected Time and for the Xaxis we selected Excess Return vs. United States. We converted plot symbols to lines. Theseoptions can be found on the right click menu (Select Axis Statistics and Convert Plot Series).Figure 4 is our Manager vs. Benchmark graph. Here we selected rolling return and set the rollingwindow at 4 quarters. To run this small window size you must first select none in the StyleBasis selection in Analysis Parameters/Summary.In all of these graphs we have used the new Dynamic Text function to change the titles andlegends to reflect the actual indexes we are using. So instead of saying Manager vs.Benchmark it says Fort Lauderdale, Fl vs. United States Return. Because we used dynamictext this title will automatically change if we select another manager and/or benchmark.To create the four tables of best and worst three and five year returns we did a search selectingall 379 cities as managers. We screened returns for the best and worst and highlighted the toptwenty for each category. From the right click menu we selected create workbook for selectedmanagers. In that workbook we added a custom table and selected the two statistics wedisplayed.